(x-3)(x+4)=x+4

Solution for (x-3)(x+4)=x+4 equation:

Simplifying
(x + -3)(x + 4) = x + 4

Reorder the terms:
(-3 + x)(x + 4) = x + 4

Reorder the terms:
(-3 + x)(4 + x) = x + 4

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) = x + 4
((4 * -3 + x * -3) + x(4 + x)) = x + 4
((-12 + -3x) + x(4 + x)) = x + 4
(-12 + -3x + (4 * x + x * x)) = x + 4
(-12 + -3x + (4x + x2)) = x + 4

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) = x + 4

Reorder the terms:
-12 + 1x + x2 = 4 + x

Solving
-12 + 1x + x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
-12 + -4 + 1x + -1x + x2 = 4 + x + -4 + -1x

Combine like terms: -12 + -4 = -16
-16 + 1x + -1x + x2 = 4 + x + -4 + -1x

Combine like terms: 1x + -1x = 0
-16 + 0 + x2 = 4 + x + -4 + -1x
-16 + x2 = 4 + x + -4 + -1x

Reorder the terms:
-16 + x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
-16 + x2 = 0 + x + -1x
-16 + x2 = x + -1x

Combine like terms: x + -1x = 0
-16 + x2 = 0

Factor a difference between two squares.
(4 + x)(-4 + x) = 0

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Solution
x = {-4, 4}